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Abstract:

A method for polishing lens surfaces, in which a) prior to the polishing
process, for the purpose of determining an abrasion profile, at least one
point of a workpiece is polished by means of a polishing tool to be used,
using at least one pre-defined parameter; b) the polishing abrasion thus
achieved on the workpiece side is determined by measuring; c) on the
basis of the abrasion profile, at least one parameter is set for a
subsequent polishing process, and the polishing process is completed at
least partially. A method for polishing lens surfaces, in which the
polishing point is places at least outside of the workpiece centre at a
distance a from a plane which is tensioned by the tool spindle axis and
the workpiece spindle axis. The invention furthermore relates to a lens
polishing machine in which at least one movement axis is provided, by
means of which a distance a between the polishing point and a plane which
is tensioned by the tool spindle axis and the workpiece spindle axis can
be set and/or changed.

Claims:

1. A method for polishing lens surfaces in which a polishing area of a
polishing head which rotates around a tool spindle axis is guided over
the lens surface to be polished of a workpiece, wherein at least one
parameter is set for this polishing process, comprising the steps of:a)
prior to the polishing process, for the purpose of determining an
abrasion profile, polishing at least one polishing zone PL of a workpiece
by means of a polishing tool to be used, using at least one pre-defined
parameter;b) the polishing abrasion thus achieved on the workpiece side
is determined by measuring;c) determining an abrasion profile from the
polishing abrasion;d) on the basis of the abrasion profile, setting at
least one parameter for a subsequent polishing process, and completing
the polishing process at least partially.

2. A method for polishing lens surfaces in which a polishing area of a
polishing head which rotates around a tool spindle axis is guided over
the lens surface to be polished of a workpiece which rotates around a
workpiece spindle axis, wherein the polishing tool and the workpiece are
positioned against each other in a polishing point P, comprising the
steps of:placing the polishing point P at least outside of the workpiece
centre at a distance a from a straight line G which connects the tool
spindle axis and the workpiece spindle axis, wherein the straight lines G
and the polishing point P are arranged on a shared section plane S.

3. The method according to claim 2, wherein on the tool side, a movement
vector V of the polishing movement is set, andi) at least one direction
component of the movement vector V runs in the radial direction to the
lens and/orii) the direction of the movement vector V is varied during
the polishing process.

4. A method for polishing lens surfaces in which a polishing area of a
polishing head which rotates around a tool spindle axis is guided over
the lens surface to be polished of a workpiece which rotates around a
workpiece spindle axis, comprising the steps of:positioning the polishing
tool and the workpiece against each other in a polishing point P, and
guiding the polishing point P on the tool side in the radial direction
during the polishing process, from the outside inwards towards the tool
spindle axis, or from the inside outwards.

5. The method according to claim 1, wherein the polishing point P is
guided on the workpiece side in the radial direction during the polishing
process, from the outside inwards towards the workpiece centre.

6. The method according to claim 1, wherein the direction of a movement
vector V is set in the polishing point P in such a manner that it runs in
the radial direction to the workpiece from the inside outwards.

7. A lens polishing machine comprising: a polishing spindle which
comprises a tool spindle axis for holding a polishing head and with a
workpiece spindle which comprises a workpiece spindle axis for holding a
lens to be polished, wherein the polishing head and a lens surface of the
lens can be brought into contact against each other in a polishing point
P, wherein at least one movement axis B1 is provided, by means of which a
distance a between the polishing point P and a straight line G which
connects the tool spindle axis and the workpiece spindle axis can be set
and/or changed, wherein the straight line G and the polishing point P are
arranged on a shared section plane S.

8. The lens polishing machine according to claim 7, wherein the movement
axis B1 is designed as a translation axis, and a further movement axis B2
is provided which is designed as a pivot axis, which encloses a right
angle with a direction portion of the movement axis B1, wherein the
movement axes B1 and/or B2 comprise a direction portion which is at right
angles to the workpiece spindle axis.

9. The lens polishing machine according to claim 7, wherein a further
movement axis B3 is provided which is designed as a translation axis,
which comprises a direction portion, which encloses a right angle with
the movement axis B1 and/or with the movement axis B2, wherein the
movement axis B3 comprises a direction portion which is parallel to the
workpiece spindle axis.

10. The lens polishing machine according to claim 7, wherein by means of
the movement axes B1, B2 and/or B3, the distance a can be set
independently of a position of the polishing point P on the tool side.

11. The method according to claim 2, wherein the polishing point P is
guided on the workpiece side in the radial direction during the polishing
process, from the outside inwards towards the workpiece centre.

12. The method according to claim 4, wherein the polishing point P is
guided on the workpiece side in the radial direction during the polishing
process, from the outside inwards towards the workpiece centre

13. The method according to claim 2, wherein the direction of a movement
vector V is set in the polishing point P in such a manner that it runs in
the radial direction to the workpiece from the inside outwards.

14. The method according to claim 4, wherein the direction of the movement
vector V is set in the polishing point P in such a manner that it runs in
the radial direction to the workpiece from the inside outwards.

15. The lens polishing machine according to claim 8, wherein a further
movement axis B3 is provided which is designed as a translation axis,
which comprises a direction portion, which encloses a right angle with
the movement axis B1 and/or with the movement axis B2, wherein the
movement axis B3 comprises a direction portion which is parallel to the
workpiece spindle axis

16. The lens polishing machine according to claim 17, wherein by means of
the movement axes B1, B2 and/or B3, the distance a can be set
independently of a position of the polishing point P on the tool side.

Description:

FIELD OF THE INVENTION

[0001]The invention relates to a method for polishing lens surfaces, in
which a polishing area of a polishing head which rotates around a tool
spindle axis is guided over the lens surface of a workpiece which is to
be polished, wherein the polishing area and the lens surface are in
contact only in a partial section, the polishing point, and at least one
parameter is set for this polishing process. The following variables are
feasible as parameters for the polishing process: the rotational speed of
the polishing head, the rotational speed of the workpiece, i.e. the
relative speed, the position of the polishing point (contact point) on
the polishing area of the polishing head, the position of the polishing
point (contact point) on the lens surface, the polishing pressure or
polishing force, the relative position between the polishing point, tool
axis and workpiece axis, in particular the direction and level of the
relative speed or movement vector V from tool to workpiece and/or the
degree or time progression of the change in one or more pre-specified
variables during the polishing process.

[0002]Furthermore, the invention relates to a method for polishing lens
surfaces in which a polishing surface of a polishing head which rotates
around a workpiece spindle axis is guided over the lens surface which is
to be polished of a workpiece which rotates around a workpiece spindle
axis, wherein the tool and the workpiece are only positioned against each
other in a partial section, the polishing point P.

[0003]Finally, the invention relates to a lens polishing machine with a
polishing spindle which comprises a workpiece spindle axis, for holding a
polishing head which can be rotationally driven via the workpiece spindle
axis, and with a workpiece spindle comprising a workpiece spindle axis
for holding a lens to be polished, wherein the polishing head and a lens
surface of the lens can only be brought into position against each other
in one polishing point P.

BACKGROUND OF THE INVENTION

[0004]In lens technology, a differentiation is made between two areas of
application and two categories of lens: optics, for which lenses made of
mineral glass with spherical surfaces are usually used, and spectacles,
for which lenses made of synthetic material with aspherical and
non-rotationally symmetrical surfaces are usually used. The latter
surfaces are polished using a polishing head with a zonally effective
polishing method due to the lack of rotational symmetry, by contrast to
which the spherical surfaces of the mineral glass lenses are polished all
over with a polishing tool which has the required sphere. Additionally,
it is provided that the spherical surfaces of the mineral glass lenses
are polished zonally for the purpose of correcting the overall polishing
procedure. For this purpose, a polishing head with a flexible polishing
surface is usually used which serves to polish local ridges.

[0005]A method for polishing an aspherical, rotationally symmetrical
surface of a lens by means of a tool which rotates around a tool axis is
already known from DE 10 2004 047 563 A1. The workpiece is contacted in
an area of a workpiece surface by an area which contacts it momentarily
in each case, which is at least one partial area of an area to be
machined, which is itself a partial area of a polishing area of the tool,
wherein the tool axis penetrates a polishing area and the position of the
tool is set in such a manner that the centre of the area of the tool
which contacts the workpiece momentarily in each case (the polishing
point) lies to the side of the tool axis. Here, it is provided that a
tool with an even polishing area is tipped depending on a surface
perpendicular of the workpiece in the area which is contacted, around an
axis which differs from the tool axis, wherein the tool axis is aligned
parallel to the surface perpendicular, and the tool is displaced parallel
a workpiece surface in the area which is contacted. In the outer areas of
the workpiece, i.e. outside the centre, the polishing capacity is
controlled via the rotational speed. A variation of the radius of the
polishing point on the tool side is not provided when machining the outer
areas of the workpiece.

[0006]With reference to a section plane S which comprises the polishing
point, the polishing point and the two section points SW and SL lie
between the tool axis and the section plane S and between the workpiece
axis and the section plane S on a straight line. Accordingly, the
polishing point lies in the plane E which is tensioned by the tool axis
and the workpiece axis.

[0007]A polishing device is known from EP 1 384 553 A2. This comprises a
polishing head with a rotational axis, a pivot axis which is arranged at
right angles to it, and a further pivot axis which is arranged vertically
to both aforementioned axes. The polishing head can thus be rotated
around all three spatial axes. On the workpiece side, a rotational axis
is also provided. The polishing point, which can be generated, can thus
be placed on the tool side decentrally to the rotational axis of the
polishing head.

[0008]With reference to a section plane S which comprises the polishing
point, the polishing point and the two section points SW and SL are in
contact between the tool axis and the section plane S, and between the
workpiece axis and the section plane S, or on a connecting straight line
G, i.e. the straight line G passes through the polishing point. The
polishing point comprises no distance a to the straight line G. When the
tool axis and the workpiece axis tension a plane E, the polishing point
lies in the centre on this plane E, or centrally to the straight line G.
In this case, the polishing point also comprises no distance a to the
plane E or to the straight line G.

SUMMARY OF THE INVENTION

[0009]The object of the invention is to design a polishing method for
polishing optically effective lens surfaces in such a manner that a
polishing abrasion which is as defined as possible is guaranteed, and
with a polishing capacity which is overall as low as possible, the best
possible polishing result is achieved.

[0010]The object is attained according to the invention by means of a
method, and by means of a lens polishing machine according to the claims.

[0011]For the polishing head, or type of polishing head, selected by the
user, an abrasion profile for the polishing capacity or polishing
abrasion thus to be attained for it is calculated experimentally, so that
the anticipated polishing capacity or polishing abrasion is known for
subsequent polishing processes with this type of polishing head, at least
for the parameters used. The required polishing abrasion or polishing
capacity can thus be set to a high degree of precision and reproduced.
For this purpose, prior to the polishing process and in order to
determine the abrasion profile, at least one partially circular polishing
zone PL of a workpiece of the type of workpiece or lens to be used is
polished by means of a polishing tool of a polishing tool type to be used
and a polishing agent type, applying at least one parameter, or different
pre-defined parameters. Then, the polishing abrasion which is thus
achieved on the workpiece side is determined using measurements, from the
polishing abrasion, an abrasion profile or abrasion characteristic is
determined, and on the basis of the abrasion profile, at least one
parameter, or the parameters, are set for a subsequent polishing process.
Subsequently, the required polishing process can be at least partially
completed, wherein the required polishing capacity can be highly
precisely set due to the determined abrasion profile for the polishing
head type used, and for the lenses to be polished on the basis of the
method or fundamental principles described below. The recording of
measurements preferably includes the measurement of the height and width
or of the diameter of the polished zone of the workpiece or lens surface.

[0012]The rotationally symmetrical lens surface can be polished with a
rotationally symmetrical polishing tool. The polishing point (contact
area) between the lens and the polishing tool can here lie in the centre
of the polishing tool or also with radius PW at any point on the
polishing area of the polishing tool. The projection of the rotationally
symmetrical lens surface to be polished is assumed below to be lying on
the X-Y plane of a Cartesian coordinate system. A change in the height of
the area then corresponds to a change in the Z direction.

[0013]The polishing tool is then guided over the lens surface in such a
manner that with an infinitely small polishing point, the tool spindle
axis runs parallel to the perpendicular in the polishing point on the
lens surface.

[0014]The calculation of the abrasion profile or dwell time profile or
feed profile of the polishing tool is then made on the basis of the
following assumptions:

[0015]The abrasion characteristic at one point on the lens is
proportionate to the relative speed between the lens surface and the
polishing area of the tool at this point

[0016]The abrasion characteristic at a point on the lens is proportionate
to the force which the polishing tool applies in this point to the lens
surface

[0017]The characteristic of the polishing tool is approximated to that of
an ideal spring, i.e. the immersion depth on the tool side is
proportionate to the application force which normally acts in the
polishing point.

[0018]Initially, the surface projected onto the X-Y plane is dissected
into n equidistant circular rings. The circular rings are in turn
dissected into na circular ring segments. The number of circular rings_n
is here selected in such a manner that with the same circular ring width,
a sufficient number of circular rings m can be distributed on the
polishing tool diameter.

[0019]Now the polishing tool, with the polishing point (rPj) with the
radius on the tool side or distance_rPj between the polishing point and
the centre of the polishing tool, on a circular ring, is brought into
contact with the radius_rLi=X, and is immersed by a degree_d. Then, on
the basis of the local geometry of the lens and the polishing tool in
dependence on the immersion depth d, the force distribution of the
circular ring elements which are in contact is determined. Here,
initially, a random spring constant_k is used. Then, the relative speed
between the polishing tool and the lens is calculated for each circular
ring element which is in contact. This is now conducted taking into
account the size of the area on the lens which corresponds to the
corresponding circular ring segment on the X-Y plane. Due to the fact
that the lens moves along below the polishing tool nL*t_times, depending
on the torque_nL in the time_t, from the variables determined thus far,
the relative speed and polishing force for each circular ring segment, a
two-dimensional local abrasion profile or abrasion rate for the circular
rings of the lens with a fixed position of the polishing tool for a dwell
time_t, and for rLi, rPj, nL, nP and d, wherein the polishing point
comprises a maximum width of m_circular rings. Here, nP is the torque of
the tool and d is the immersion depth of the polishing tool.

[0020]Now the above calculation is repeated for all possible polishing
points (rLi) on the workpiece side with the radius or distance_rLi on the
lens. Thus, n local abrasion profiles=f(t, rLi, rPj, nL, nP, d, k) are
obtained.

[0021]The model described above thus far contains the kinematic and
geometric properties of the process. On the assumption that the abrasive
properties of the polishing agent and the material properties of the
polishing tool can be described by the spring constant_k still randomly
selected above, this is now determined by comparing a local abrasion
profile determined experimentally with n measuring positions_×s for
a time is in comparison with that theoretically calculated with n(xs).

[0022]With the spring constant_k thus gained experimentally for this
process, the n local abrasion profiles now result which are relevant to
the calculation.

[0023]The determination of a dwell time profile for a global abrasion
function for a movement along the X axis (radial movement) over the
n_circular rings of the lens can now be determined with the aid of the
time standardised local abrasion functions by means of a minimisation
method.

[0024]Advantages of the model:

[0025]The model takes into account the kinematics and the geometry of the
process

[0026]The abrasive properties of the polishing agent which can
theoretically only be recorded with difficulty, and the material
properties of the polishing tool, are traced back to the spring
constant_k of the polishing tool, and are obtained from an experimentally
determined local abrasion profile.

[0027]Thus, the model provides any dwell time profile required from just
one experimentally determined local abrasion profile.

[0028]According to the invention, the polishing point P is placed at least
outside of the centre of the workpiece at a distance a to a straight line
G which connects the tool spindle axis and the workpiece spindle axis,
wherein the straight line G and the polishing point P are arranged on a
shared plane S. When the tool spindle axis and the workpiece spindle axis
tension a plane E, the distance a relates to the plane E which is
tensioned by the tool spindle axis and the workpiece spindle axis. The
distance a guarantees a polishing process with a movement vector V which
runs in the radial direction to the workpiece. Since the lenses to be
polished are usually machined in the circumferential direction during
manufacture, the movement vector V of the polishing tool, which according
to the invention is aligned in the radial direction, guarantees an
optimum polishing result. A reinforcement of the grooves or scores to be
polished is prevented by the radial polishing movement. When the distance
a of the polishing point, which is usually bordered by a round, oval or
ring-shaped line, is determined, a set-down is to be made on the
geometric centre of the polishing point or alternatively, on the edge of
the polishing point. The section plane S comprises both with the tool
spindle axis and with the workpiece spindle axis a section point SW or
SL, wherein the polishing point P is arranged at a distance a in relation
to the connecting straight line G contained in the section plane S of the
two section points SW and SL.

[0029]For this purpose, it can also be advantageous when on the tool side,
a movement vector V of the polishing movement is set, and

i) at least one direction component of the movement vector V runs in the
radial direction to the workpiece or to the lens, and/orii) the direction
of the movement vector V is varied during the polishing process. For the
purpose of varying the polishing capacity, a variation of the movement
vector V is helpful, in particular when the rawness of the lens surface
originating from the grooves and scores varies according to the
alignment.

[0030]The tool and the workpiece preferably turn in the same direction, so
that when the polishing zone PW or its radius RW on the tool side is
reduced in size, and when the size of the polishing zone PL or its radius
RL is reduced on the workpiece side, a clear reduction of the polishing
capacity to be applied ensues.

[0031]Due to the fact that according to the invention, the polishing point
P is guided on the tool side during the polishing process in the radial
direction from outwards to inwards, or from inwards to outwards, the
polishing point P runs in spiral form from the edge area inwards towards
the tool spindle axis, or vice-versa. Thus, the polishing capacity can be
varied by changing the radius RW of the polishing point P. At the same
time, the polishing area of the polishing head is almost completely and
evenly utilised in relation to the polishing area, which guarantees the
reproducibility of the polishing process with a defined polishing
abrasion. Thus, a radius RW of the polishing point or the polishing zone
PW is changed on the tool side. The radius RW varies between 1% and 100%
of the tool radius or polishing head radius. The polishing point P can be
guided over the length of the tool radius either constantly or
inconstantly, i.e. the radius RW can also be constantly or inconstantly
changed during the polishing process within the aforementioned % range,
or maintained at a constant for certain periods of time.

[0032]Alternatively, on the tool side, the size of the radius R of the
lens can be selected as the maximum radius RW of the polishing zone PW.
Thus, the polishing point completes almost the same radius RW or RL on
the tool side and on the workpiece side, i.e. from the edge into the
centre of the lens, or almost to the tool spindle axis. When the radius
RW or RL remains the same, the reproducibility of the polishing abrasion
or polishing process can be improved.

[0033]Accordingly, it can be advantageous when the polishing point P is
guided in the radial direction from the outside inwards towards the
centre of the workpiece on the workpiece side during the polishing
process. The polishing point P in this case runs spirally inwards from
the edge area towards the centre of the workpiece. Here, a radius RL of
the polishing point is smaller on the workpiece side. Since the workpiece
is usually completely machined, the radius RL of the polishing point
moves over the entire workpiece radius.

[0034]The polishing capacity required on the lens surface grows with the
radius on the workpiece side, so that the outer area of the lens is
machined using a large radius on the tool side. The further the polishing
point moves into the centre of the lens, or the smaller the radius RL of
the polishing zone on the workpiece side, the smaller the radius RW of
the polishing zone is selected on the tool side. Thus, on the one hand,
the polishing capacity is distributed over almost the entire tool area or
polishing area. On the other, the polishing capacity is reduced towards
the centre of the lens, since the polishing capacity reduces with the
decreasing radius RW (with the same torque of the polishing head and the
same polishing pressure). The centre of the lens can thus be machined
with a lower polishing capacity, since a different polishing zone of the
polishing head with a smaller radius RW is used, without having to change
the torque of the polishing head or the polishing pressure.

[0035]It can be of particular significance for the invention when the
direction of the movement vector V is set in the polishing point P on the
tool side in such a manner that it runs in the radial direction to the
workpiece from the inside outwards. Thus, in particular when machining
the outer zone of the lens surface, the polishing agent which is applied
in the area of the centre onto the lens surface to be polished, or onto
the polishing area, is in addition to the centrifugal force guided
outwards towards the polishing point P through the polishing movement on
the tool side. The polishing capacity to be obtained is thus maximised.

[0036]In connection with the design of the lens polishing machine
according to the invention, it is advantageous when at least one movement
axis B1 is provided, by means of which a distance a of the polishing
point P to a straight line G which connects the tool spindle axis and the
workpiece spindle axis can be set and/or changed, wherein the straight
line G and the polishing point P are arranged on a shared plane. When the
tool spindle axis and the workpiece spindle axis tension a plane E, the
distance a relates to the plane E which is tensioned by the tool spindle
axis and the workpiece spindle axis. When determining the distance a,
set-down is made on the edge of the polishing point or the contact point.
When a distance a is set, the movement vector V of the polishing head can
be set in such a manner that it comprises at least one direction
component radial to the lens. Thus, an improvement in the polishing
result ensues, since grooves and scores which run in the circumferential
direction in particular are polished in a direction transverse to it.

[0037]The section plane S comprises both with the tool spindle axis and
the workpiece spindle axis a section point SW or SL, wherein the
polishing point P is arranged at the distance a in relation to the
connecting straight line G on the section plane S of the two section
points SW and SL.

[0038]For this purpose, it can be advantageous when the movement axis B1
is designed as a translation axis, and a further movement axis B2 which
is deigned as a pivot axis is provided, which encloses a right-angle with
a with a direction portion, wherein the movement angle B1 and/or B2
comprise a direction portion at right-angles to the workpiece spindle
axis. The movement axis B1 can also be designed as a pivot axis with a
translation portion.

[0039]It can also be advantageous when a further movement axis B3 is
provided, which is designed as a translation axis, which comprises a
direction portion which encloses a right-angle with the movement axis B1
and/or with the movement axis B2, wherein the movement axis B3 comprises
a direction portion parallel to the workpiece spindle axis. The movement
axis B3 can also be designed as a pivot axis with translation portion.

[0040]Here, it can be advantageous when by means of the movement axis B1,
B2 and/or B3, the distance a can be set independently of a position on
the tool side of the polishing point P. The position of the polishing
point on the tool side, i.e. the radius RW of the polishing point or
polishing zone, can be selected independently of the setting or variation
of the distance a. Thus, the parameters of the polishing process can be
selected according to the required polishing process.

BRIEF DESCRIPTION OF THE DRAWINGS

[0041]Further advantages and details of the invention are explained in the
patent claims and in the description, and shown in the drawings, in
which:

[0042]FIG. 1 shows a schematic diagram of the lens polishing machine;

[0043]FIG. 2a shows a schematic diagram of the geometric proportions;

[0044]FIG. 2b shows a schematic diagram according to FIG. 2a with a
changed polishing point;

[0045]FIG. 2c shows an enlarged schematic diagram according to FIG. 2b
with a changed polishing point;

[0046]FIG. 3 shows a schematic diagram of the geometric proportions.

[0047]The lens polishing machine 1 shown schematically in FIG. 1 comprises
a polishing spindle 2 with a polishing head 5 arranged thereon and a
workpiece spindle 3 with a workpiece or a lens 4 arranged thereon. Both
the polishing head or polishing tool 5 and the lens 4 are freely
interchangeable.

DETAILED DESCRIPTION OF THE INVENTION

[0048]The polishing head 5 can be rotated around a tool spindle axis 2.1,
while the workpiece spindle 3 can be rotated with the lens 4 around a
workpiece spindle axis 3.1. In order to guarantee a polishing process,
the polishing head 5 lies with its polishing surface 5.1 in the polishing
point P against a lens surface 4.1 of the lens 4. Due to the fact that
both the polishing head 5 and the lens 4 rotate around the tool spindle
axis 2.1 or workpiece spindle axis 3.1, a circular ring-shaped polishing
zone PW is created on the polishing surface 5.1 and a polishing zone PL
which is also circular ring-shaped is also created on the lens surface
4.1. A prerequisite for this is that both on the tool side and on the
workpiece side, a radius RW or RL of the polishing point P is not
changed.

[0049]In order to vary the radius RW on the tool side of the polishing
zone PW on the one hand, and to vary the radius RL of the polishing zone
PL on the workpiece side on the other, the polishing spindle 2 comprises
three movement axes B1, B2, B3. The movement axis B3 is designed as a
translation axis, and runs parallel to the workpiece spindle axis 3.1.
The movement axis B1 is also designed as a translation axis, and runs at
right-angles to the translation axis B3. The movement axis B2 is designed
as a pivot axis and encloses a right-angle with both the movement axis B3
and the movement axis B1.

[0050]In the position shown in FIG. 1, the workpiece spindle axis 3.1 and
the tool spindle axis 2.1 tension a plane E, wherein the polishing point
P comprises a distance a to the plane E. The distance a relates to a
direction at right-angles to the plane E. The workpiece spindle axis 3.1
and the tool spindle axis 2.1 here enclose an angle α.

[0051]In FIGS. 2a to 2c, the application proportions between the polishing
head 5.1 and the lens surface 4.1 are shown in simplified form in the top
view in relation to a section plane S. The polishing point P is arranged
in the section plane S, wherein the section plane S sections both the
workpiece spindle axis 3.1 at the section point SL and the tool spindle
axis 2.1 in the section point SW. Within the section plane S, a
connecting straight line G is shown between the tool spindle axis 2.1 and
the workpiece spindle axis 3.1, which shows a section line between the
section plane S and the plane E according to FIG. 1. The polishing point
P is at the distance a from the connecting straight line G. According to
the embodiment shown in FIGS. 2a to 2c, it is not absolutely necessary
that the tool spindle axis 2.1 and the workpiece spindle axis 3.1 tension
a plane E. The two axes can also be arranged askew to each other, wherein
in all cases, the connecting straight line G is provided within the
section plane S.

[0052]According to the view shown in FIG. 2a, the polishing zone PW on the
tool side comprises a radius RW which approximately corresponds to the
radius R1 of the polishing head 5. A similar principle applies to the
radius RL of the polishing zone PL on the workpiece side. The radius RL
also approximately corresponds to the radius R2 of the lens 4. The lens 4
is machined from the outside inwards towards the workpiece centre 4.2,
starting from the edge 4.3 in relation to the progression of the
polishing point P or the progression of the radius RL of the polishing
zone PL, which is shown as an example in FIGS. 2a to 2c for different
radii RL. The same applies accordingly to the progression of the
polishing point P or the radius RW of the polishing zone PW on the tool
side. The polishing point P is accordingly guided towards the tool centre
or workpiece spindle axis 3.1, starting from the edge 5.3 of the
polishing head 5.

[0053]Due to the distance a provided between the polishing point P and the
connecting straight line G or the plane E, as explained above, the
polishing head 5 or polishing area 5.1 comprises a movement vector V
which runs according to FIGS. 2a to 2c in the radial direction to the
lens 4. By varying the distance a, the direction of the movement vector V
can be changed as required. When the distance a is zero, the movement
vector V necessarily runs in the circumferential direction to the lens 4.

[0054]According to the view shown in FIG. 2c, which for reasons of clarity
is shown in somewhat larger form than the views shown in FIGS. 2a and 2b,
it can be seen that during the polishing process, the radius RL or RW of
the polishing zone PL on the workpiece side or the polishing zone PW on
the tool side is smaller as the polishing machining progresses, so that
with the same torque remaining of the tool 5 and the workpiece 4 on the
one hand, and with the same polishing pressure remaining on the other,
the polishing capacity achieved overall in the polishing point P is also
lower, which is advantageous particularly in the area of the workpiece
centre 4.2, i.e. the centre of the lens 4.2. Both the lens 4 and the
polishing area 5.1 of the polishing head 5 are machined or used over
their entire area due to the polishing process described above.

[0055]According to the method shown in FIG. 3, the radius RW of the
polishing zone PW on the tool side is at the beginning of machining the
same size as the radius RL of the polishing zone PL on the workpiece
side. During machining, the radius RW and the radius RL are reduced in
size to the same degree. On the workpiece side, the radius RW is reduced
to zero, and on the tool side, the radius RL is reduced to 1% of the
radius R1 of the polishing head, or until it is close to the tool spindle
axis 2.1.